The Kansas School Naturalist is sent upon request, free of charge, to Kansas teachers, school board members arid administrators, librarians, conservationists, youth leaders, and other adults interested in nature education. Back numbers are sent free as long as the supply lasts, except Vol. 5, No.3, Poisonous Snakes of Kansas. Copies of this issue may be obtained for 25 cents each postpaid. Send orders to The Kansas School Naturalist, Department of Biology, Kansas State Teachers College, Emporia, Kansas.

The Kansas School Naturalist is published in October, December, February, and April of each year by The Kansas State Teachers College, 1200 Commercial Street, Emporia, Kansas. Second-class postage paid at Emporia, Kansas.

Left to right: Mrs. Carter, Mr. Hagen, Mrs. Parkman. THIS ISSUE OF The Kansas School Naturalist was produced by Ruby M. Corter and Margaret C. Parkman, members of the second section of the 1966 Workshop in Conservation. The second section of the annual workshop, open only to persons who have teaching experience and an established interest in conservation and science education, is devoted to the production of teaching aids. The 1966 workshop was directed by Scott D. Hogen, who now teaches biology at the University of Akron at Akron, Ohio.

It is with extreme regret that we announce the death on November 18 of Miss Helen M . Douglass, member of our editorial board since the beginning. Further details will be given in the February number, which will be designated as the Helen M. Douglass Memorial Issue.

Time and Velocity

by Ruby M. Carter, Yates Center High School and Margaret C. Parkman, Olpe High School

"Time is the duration measured for all things with a beginning and an end, between an eternity past and an eternity future. It is a period during which an action or process continues." So says one dictionary. Says another, more simply, "time is measured, or measurable duration."

"Velocity is quickness of motion, time rate of motion, in a given direction and a given sense, and is calculated by dividing distance by time," or according to another, "swiftness."

In this issue of The Kansas School Naturalist we present some aspects of the measurement of time and velocity that we hope will be useful to teachers.

MAN'S EARLY ATTEMPTS TO MEASURE TIME

Man's first awareness of time probably was that period between daylight and darkness, and his first effort to record or mark the passage of time for future reference was thus geared to the rotation of the earth. When man needed to mark longer periods of time he used the recurring phases of the moon and many of his activities were related to the full moon. The seasonal changes of the year and its effects upon the plant and animal life about early man gave him a longer measure of time.

Early attempts to mark the passage of time may have been only marking the shadows cast by rocks and trees. Sunlight falling through certain openings at Stonehenge in England, gave ancient Celts the assurance that longer and warmer days necessary for planting and harvesting crops would soon arrive. Some early timing devices are pictured in Figures 1 to 4.

TIME UNITS

Through the course of the centuries man has developed many different units for expressing the amount or duration of time. A few of these are shown below:

60 seconds

1 minute

60 minutes

1 hour

24 hours

1 day

7 days

1 week

14 days

1 fortnight

29 1/2 days

1 lunar month

12 months (solar)

1 year

365 days, 5 hours, 48 min. 7 sec.

1 solar year

10 years

1 decade

100 years

1 century

1000 years

1 millennium

The above list includes such units as day, month, year; we ordinarily think of these as simple terms the meanings of which are clear to everyone. But not so, as may be seen from the following descriptions of several different kinds of days, months, and years.

Figure 1 (upper left)-Sundial, accurate to 6 or 7 minutes. The shadow of the gnomon rod falling on the curved gnomon gives a more accurate reading of time than a dial with flat surfaces might .give. The gnomon rod is placed parallel to the earth's axis to compensate for the tilt of the earth on its axis.

Figure 2 (upper right)-Water Clock or Clepsydra. A measured flow of water marked the passage of 24 hours. The float on the water in the beaker pushed a notched rod upward and rotated the cogwheel one notch at a time . The clock face showed the hour of the day. At the end of 24 hours the water container was emptied and the cycle started over again.

Figure 3 (lower left)-Fire Clock. Candles with evenly-spaced rings were burned day and night. When the candle burned from one ring to another a unit of time had passed.

Figure 4 (lower right)-Sand Clock or Hour Glass. Sand flowed through a small opening between the bowls. The glass was turned over to mark the beginning of a new timing period. The hour gloss or sand clock was commonly used to measure short periods of time.

Sidereal day - the time required for a point on earth to complete two successive passages in relation to any star other than the sun: 23 hours, 56 minutes, 4.09 seconds.

Solar day - the average time interval from midnight to midnight: also called the natural day: 24 hours.

Anomalistic month - one revolution of the moon, measured from one perigee (point in the orbit of the moon nearest the earth) to the next: 27 days, 13 hours, 18 minutes, 33.2 seconds.

Draconitic month - the time interval be¬tween two nodes (points where the orbit of the moon intersects the plane of the earth's orbit) of the moon 's orbit; also called the nodical month: 27 days, 5 hours, 5 minutes, 36 seconds.

Lunar month - the time required for the moon to complete one revolution around the earth, measured from the passing of two similar phases of the moon; also called the synodic month: 29 days, 12 hours, 44 minutes, 2.9 seconds.

Sidereal month - the time required for one revolution of the moon about the earth, measured by two successive passages of the moon past a selected star: 27 days, 7 hours, 43 minutes 12 seconds.

Anomalistic year - one revolution of the earth, measured from one perihelion (point in the orbit of the earth nearest the sun) to the next: 365 days, 6 hours, 13 minutes, 53 seconds.

Astronomical year - the time required for one complete revolution of the earth around the sun, as reckoned from two successive passages of a point on earth relative to the Vernal Equinox; also called the tropical year: 365 days, 5 hours, 48 minutes, 45.51 seconds.

Eclipse year - the time interval between two successive conjunctions of the sun with nodes of the moon's orbit: 365 days, 14 hours, 52 minutes, 53 seconds.

Leap year - the special year of 366 days; which comes every fourth year, resulting from the fact that the common year of 365 days is about one fourth day shorter than the astronomical year.

Sidereal year - the time required for one complete revolution of the earth around the sun, relative to a selected star: 365 days, 6 hours, 9 minutes, 9.54 seconds.

THE CALENDAR

The calendar is a system of fixing the divisions of time (years, months, weeks, days) for the observance of religious events and the conduct of civil affairs. The calendar is based on the cycle of the seasons and the recurrent phases of the moon. The common year and the astronomical year do not coincide exactly in length, and this causes discrepancy in the calendar.

The Assyrians, ancient Greeks, and Romans developed calendars based on the common year of 365 days, and when the calendars went out of step with the cycle of the sea¬sons, they inserted an extra month.

By the time Julius Caesar came into power, January fell in the autumn. In 45 B.C., Caesar reformed the calendar and established the Roman year of 365 1/4 days. With three years of 365 days and a leap year of 366 days every four years, this calendar compensates for the fraction of a day. But the fraction is not exactly one fourth of a day; the actual difference is 5 hours, 48 minutes, 45.51 seconds; so a leap year every four years is too many.

The difference between the Julian calendar and the solar year amounted to ten days by 1582. In effort to keep the seasons in the proper place, Pope Gregory XII dropped ten days from the calendar and modified the leap year system to allow for 97, rather than 100 leap years every four centuries.

Several other calendars besides the widely accepted Gregorian calendar, are in use. The Eastern Orthodox Church still used the Julian calendar; the Jewish calendar is a combination of the lunar-solar systems, and the Moslem calendar of Hegira is still in use.

Calendar reform, suggested primarily to provide a system whereby dates can be stabilized from year to year and can be memorized, is under study by the United Nations. Sponsored by the World Calendar Association, this method is based upon the division of the year in four equal quarters', with the first month in each quarter having 31 days and the remaining two having 30 days. The 365th, or "year-end" day is to be inserted between December 30 and January 1. In leap years an extra day, World Day, is interposed after June 30. To date support for the reform has not been sufficient to insure its accomplishment. (Figure 5)

Figure 5. The proposed world calendar provides for four equal quarters of 91 days each, plus a year-end day not counted in any quarter. In the present calendar the first quarter has 90 days (91 in leap year), the second has 91, and the third and fourth have 92 each. All holidays and special dates would come on the same day of the week and of the month each year.

Figure 6. The sextant was one of the earliest devices used to relate time to velocity.

LATITUDE, LONGITUDE, AND TIME ZONES

The sextant (Figure 6) is an instrument for measuring the angular distance between two points, such as the sun and the horizon. It is used most commonly by sailors for determining the position of a ship at sea. Using the sextant to Sight the placement of the sun, moon, or stars, a system for locating ships upon the surface of the ocean was developed.

Lines of latitude and longitude are drawn on the map. Every circle contains 360 degrees, as does the imaginary great circle around the earth, the equator, and the parallels drawn to it, which measure degrees of latitude. Lines drawn on the globe or map from the north pole to the south pole are meridians of longitude and measure distances east or west. On most maps or globes the meridians are drawn at 15-degree intervals, or 24 intervals in the entire circle. This is a convenient number to use as it indicates that the earth rotates fifteen degrees in one hour. Since the earth rotates west to east, the sun apparently passes from east to west.

The time, and location of all heavenly bodies, plus exact latitude and longitude readings, are recorded in the Abridged Nautical Almanac. By transient readings and a check of the Almanac, it is possible for the navigator of a ship or plane to determine the exact location of a vessel at a specific time.

In 1884, in Greenwich, England, a group of international representatives met to agree upon International Time. Beginning with the Prime Meridian, at zero degrees longitude in Greenwich as the midpoint of the first time zone, zones were marked every fifteen degrees to the east and west; twenty-four in all. Differences in theoretical and legal boundaries were the result of conflicts caused by part of a town or trade area lying in two time zones. The legal boundaries detoured around such areas. Nearly all of Kansas is located in the Central Time Zone, but a small western portion of the state is in the Mountain Time Zone.

The International Date Line was located in mid Pacific at 180 degrees west of Greenwich, as this area was largely uninhabited and thus would avoid confusion.

Figure 7. The time zones of the United States mark off intervals of 15 degrees, or one hour, or one 24th of one period of rotation of the earth.

GEOLOGIC TIME AND RADIOACTIVE ELEMENTS

One of the most accurate methods of measuring the millions of years of geologic time involves the use of radioactive elements such as uranium and thorium, carbon-14, fluorine, tritium, and potassium-argon.

Uranium and thorium occur almost exclusively in pegmatites. After formation, regardless of chemical association, heat, pressure, or any other conditions, they disintegrate slowly into lead, invisible radiations of helium, and heat. Since it has been•shown that one gram of uranium yields 1/7,600,000 of a gram of lead in a year, the ratio of lead to the amount of uranium remaining, gives the age of the rock. Thorium and actinium can also be used.

Carbon-14 is useful in determining the age of organic materials. All living things contain a constant amount of carbon-14. When the plant or animal dies, the carbon 14 disintegrates at the rate of one-half in 5560 years, and one-half of the remainder in 5560 years, and so on until the quantity is too small for accurate calculations. Thus it is possible to measure periods up to 40,000 years with an accuracy of plus or minus one percent.

Fluorine is also found in fossils; the older the fossil, the more fluorine its contains. Thus it is especially useful for determining the relative ages of fossils found in the same locality.

Tritium is the heavy, unstable isotope of hydrogen which is produced in the atmosphere by cosmic radiation and is precipitated to the surface of the earth by rain. Tritium's half-life is only 12.5 years, therefore it is useful only for comparatively short periods such as in the study of movements of water masses, either ocean currents or underground water.

VELOCITY

Velocity is a term used to express the rate at which bodies change positions in space. It is expressed by feet per second, miles per hour, and other double units, always made up on one distance unit and one time unit. For present purposes, we may consider velocity and speed as synonyms, although there is a technical difference.

Velocity is said to be uniform when these spaces are equal; it is positively accelerated when, during each portion of time, it passes through a greater space than during the previous equal portion, as in a falling body; it is retarded, or negatively accelerated, when a smaller space is traversed in each successive unit of time, as in an automobile which is coasting to a stop.

PROBLEMS

1. Uniform velocity:A train moving at a uniform rate over 150 miles in 3 hours.

Solution:Velocity equals distance divided by time (150 divided by 3), or 50 miles per hour.

2. Variable velocity:A certain moving object starts with a velocity of 20 feet per second. The velocity changes uniformly for 4 minutes and is then 76 feet second. What is the average for the period?

Solution:The average velocity equals the initial plus the final velocity divided 2 (20 + 76) / 2 or 48 feet per second. If the object had moved at the uniform rate of 48 feet per second, it would have covered the same distance as it did in 4 minutes moving at the changing velocity.

3. Accelerated velocity:A ball which has a starting velocity of 25 feet per second, moves for 5 seconds and at the end of that period has a velocity of 75 feet per second. What is its acceleration?

Solution: Acceleration in velocity divided by time. Change in velocity: (75-25) or 50 feet per second. Acceleration: (50 divided by 5) or 10 feet per second per second. During each second that it is moving, the ball increases its velocity 10 feet per second. Note that velocity is expressed in linear units per time unit, and that acceleration is expressed in velocity units per time unit.

VELOCITY OF FALLING BODIES

There are three things to consider in studying falling bodies: the distance that the body falls, the velocity, and the acceleration. A body does not fall at the same rate throughout its fall. The velocity increases with every second that it falls. The acceleration in velocity, because it results from the force of gravity, is the same for each second. Thus the velocity of a falling body at the end of a given second is the velocity at teh beginning of that second plus the acceleration.

The acceleration due to gravity is 32.16 feet per second per second, therefore the velocity (V) at the end of the first second equals 0 + 32.16, or 32.16 feet per second.

At the end of the second second, V=32.16+32.16, or 64.32 feet per second.

At the end of the third second, V=64.32+32.16, or 128.64 feet per second, and so on; the velocity equals 32.16 x number of seconds.

The distance that a falling body travels during the first second equals the average velocity or 16.08 feet. During the next second the average velocity is 48.24 feet per second, therefore the total distance traveled during the first two seconds is 16.08 + 48.24, or 64.32 feet. Thus, the falling body gradually falls faster and faster, until it reaches a "free-fall" speed at which the air resistance is great enough to counteract the acceleration due to gravity.

For any given time in seconds the distance traveled by a falling object (not allowing for air resistance) is 32.16 t2 feet, where t is the time in seconds.

PROBLEM Distance traveled in given time:

Suppose you drop a stone from the top of a tall building and, using a stopwatch to measure the time it takes the stone to reach the ground, find that it takes 2.25 seconds. How tall is the building?

In baseball, golf, billiards, or any other ball game, the force with which the ball is struck depends upon two things, the mass (weight) of the object used for hitting, and the speed with which it is directed against the ball. The force exerted by a moving body on being stopped is proportional to its momentum, or quantity of motion.

Momentum equals mass times velocity. A body weighing 1000 pounds moving at 8 feet per second has a momentum of 8000 pound-feet per second. Of course, a body weighing 8000 pounds moving at the rate of one foot per second has exactly the same momentum. The quantity or number of units of momentum, indicates how long a body will move against a given resistance before it stops.

VELOCITY OF SOUND

Sound waves, longitudinal compression waves passing through water or air, can be heard. These waves are characterized by their period, frequency, or wave length. Period is defined as the time interval during which the source emits one Single wave or during which a propagative wave passes any given point on its way. Frequency is the number of waves emitted by the source per unit time, or the number of individual waves which pass during a unit time, through any given point. These two quantities are related by a formula:

Frequency = 1 / Period

Thus, if a wave has a period of one-hundredth of a second, a hundred waves will pass by during a one-second interval. The wave length, measured from crest to crest or from hollow to hollow, is ralted to the period or frequency of the wave and to the velocity of its propagation. The wave velocity, or the distance through which the wave motion spreads out in a time unit is equal to the number of waves emitted during that unit of the time multiplied by the length of the waves.

Wave velocity = frequency X wave length or

Wave velocity = wave length / period

The device for studying the vibration frequency or pitch of sound is a siren, a metal disc, containing a number of holes along its rim, driven at varying speeds by a motor. A steel cylinder supplies compressed air that comes out in a puff each time an opening in the rotating disc aligns with the end of the pipe releasing compressed air. If the disc rotates slowly "puff, puff," is heard. As the disc's rota¬tion velocity increases a musical tone low like a bassoon and finally high like a piccolo will be heard. As the disc rotates more rapidly, sound fades out.

Knowing the rotational velocities of the disc in each case, and the number of holes in the rim, you can calculate the number of "puffs per second" corresponding to the different sounds heard. The lowest tone the human ear recognizes as a tone is around 20 oscillations per second and the highest is nearly 20,000 oscillations per second. Figuring the velocity of sound in air, under normal atmospheric conditions as 330 meters per second, the wave lengths of audible sound are calculated to range from 1.5 centimeters to about 15 meters.

VELOCITY OF LIGHT

The first experimental attempt to measure the velocity of light, undertaken by Galileo in Florence, Italy, was negative because the one hundred-thousandth of a second delay from source to receptor is quite unnoticeable to the human senses.

Figure 8. Roemer's method of measuring the velocity of light by observing the eclipses of the moons of Jupiter.

Figure 9. Fizeau's method of measuring the velocity of light by directing a beam of light through rapidly moving spaces.

The German astronomer, Roemer, first successfully measured the velocity of light using the moons of the planet Jupiter to increase the distance covered by light by a factor of hundreds of millions. Roemer's method is illustrated by Figure 8 which shows the orbits of the Earth, Jupiter and one of its moons. The moons are periodically eclipses as they enter the broad con e of shadow cast by Jupiter. Studying these eclipses, Roemer notices sometimes they were as much as eight minutes ahead of schedule and were sometimes delayed eight minutes. The eclipses were early when the earth and Jupiter were on the same side of the sun (1st position), and delayed in the opposite case (2nd position). Ascribing correctly the changing distance between the earth and Jupiter, Roemer calculated that light must be propagated through space at a speed of about 300,000 kilometers per second (3 X 10 to the 10th cm/sec.).

The first laboratory measurement of the speed of light was carried out in 1849 by the French physicist, H. L. Fizeau (1819-1896), whose apparatus is shown in Figure 9. The apparatus consists of a pair of cogwheels set at opposite ends of a long axis. The wheels are positioned in such a way that the cogs of one are opposite the intercog openings of the other, so that a light beam from a source could not be seen by the eye no matter what the position of the wheels. If the wheels are set in fast rotation such that the wheels are moved by half the distance between the neighboring cogs during the interval of time it takes light to travel from one wheel to the other, the light is expected to pass through without being stopped. (This same principle is used on express highways for traffic signals set for uninterrupted driving at legal speeds). To observe the effect of the speed of a few thousand revolutions per minute, about the maximum Fizeau could achieve, he had to lengthen the path of the light beam by using four mirrors as shown in Figure 9. This direct laboratory measurement gave a value of the speed of light that stood in reasonable agreement with that obtained by Roemer's astronomical method.

TIME AND RELATIVITY

A man in an aircraft capable of flying around the earth in twenty-four hours, starts from some place on the equator at noon, December 2, 1966. He travels due west; six hours later he is one-quarter of the way around the earth, but the sun is still directly overhead and it is still noon, December 2, 1966. He travels on for six more hours and realizes that it is still noon, December 2. One second later he crosses the International Date Line and it is still noon but it is now December 3. If he continues his rapid journey it will be December 3 when he is three-quarters of the way around the earth and he will arrive at his starting point back on the equator at noon December 3, 1966.

If the traveler wishes to travel westward on a parallel to the equator halfway between the North pole and the equator, he will not have to travel nearly so far to return to his starting place but he must set his watch back six hours at each quarter point of his journey. Theoretically, he could travel a circle twelve feet in circumference around the North pole, then every three feet he would need to set his watch back six hours to keep "local standard time." He could stand on the North pole and select any time he wished. Time is relative to the observer's position and to the earth.

This is part of the Theory of Relativity as proposed by Einstein and it has recently been applied by Professor Robert C. Haymes, to the space craft Gemini 7. Not only did time seem to pass slowly for Fred Borman and James Lovell, it also actually did slow down some' for the astronauts. While orbiting the earth for 330 hours, Haymes figures that the astronauts aged one-thousandth of a second less than men on earth.

Haymes calculated Gemini 7's slowdown by using the formula from Einstein's 1905 Special Theory of Relativity. Time slows down for an object as its speed increases. At Gemini 7's orbital velocity of 175000 miles per hour, the effect On the astronauts was not biologically detectable.

EARTH'S TIME TABLE

ERAS

PERIODS

DEVELOPMENT OF LIFE

CENOZOIC

QUATERNARY

Appearance of manWidespread continental glaciation

TERTIARY

Rise of modern mammals and birds(Began 70 million years ago)

MESOZOIC

CRETACEOUS

Extinction of dinosaurs and many other reptile groups

JURASSIC

Domination by giant reptilesBeginning of birds and mammals

TRIASSIC

Beginning of dominance of reptiles(Began 200 million years ago.)

PALEOZOIC

PERMIAN

Extinction of many invertebrate groups and primitive type plants

PENNSYLVANIAN

Many coal forests of spore bearing plantsFirst reptiles

MISSISSIPPIAN

Abundant spore bearing plantsMany insects

DEVONIAN

First amphibiansNumerous marine fishes

SILURIAN

First land plantsFirst land animals (scorpions)

ORDOVICIAN

First indication of vertebrates (fishes)

CAMBRIAN

Invertebrates numerous and varied, trilobites dominant(Began 500 million years ago.)

PRECAMBRIAN TIME

Bacteria, algae, and a few primitive invertebrates(Began 4-5 billion years ago.)

THINGS TO DO

1. Find out in which time zone you live, What are the time zones to the east and west of you? When it is noon standard time at your home, what time is it in New York, Cleveland, Los Angeles, Anchorage, Honolulu? What time is it in London, Moscow, Bangkok, Manila? What is daylight-saving time?

2. Set an upright post three or four feet high in an exposed place and mark the position of its shadow each day at the same hour. How does the position of the shadow vary from day to day, and from month to month? How far from the base of the post is the tip of the shadow at noon, at intervals of a month? What changes occurs from sea¬son to season? During what season is the shadow shortest? When is it longest?

3. Make a sundial. Cut the cardboard as shown, with angle L equal to your latitude. Set the cardboard in a lump of clay on a flat surface such as a board. Keep the card horizontal, orient the gnomon (cardboard) in a true north-south line. Mark off the shadow positions at each hour of one sunny day and compare these positions with the shadow of the gnomon on other sunny day. (More precise directions can be found in many books.)

4. Set up a globe in such a position that its axis is pointed toward the North Star, and your state is at the top of the globe. Now the globe is in the same position relative to the sun as the earth itself. If you take the globe outdoors on a sunny day, you can see the sunrise line on the globe. Where is the sunset line? Where on the earth are children just getting ready to go to school? Where are they getting ready to go to bed?

5. Make a water clock by punching a nail hole in the bottom of a metal can filling it with water, and recording the time it takes to empty. Does the rate of dripping remain the same regardless of the amount of water in the can? What level for a half hour? How big a can, and how small a hole do you have to use to make a water clock that empties in an hour?

6. Tie a weight to a piece of string so as to make a pendulum. Make two pendulums, one with a distance of one foot between the weight and the point of support, the other .two feet. Start both swinging at the same time. How do the rates of swinging compare? How long must the pendulum be to complete a full swing in one second? Two seconds? One half second?

A FEW BOOKS

In general, "P" indicates books suitable for primary grades, "I" for intermediate grades, and "U" for upper grades and high school.

The Department of Biology presents the tenth Audubon Screen Tour Series in 1966-67. This series consists of five all-color motion pictures of wildlife, plant science, and conservation personally narrated by leading naturalists: The first two were shown in October and November. The remaining.three will be presented in Albert Taylor Hall at 7:30 p.m. on the dates listed below. Both group and single admission tickets are available: for further information write Dr. Bernadette Menhusen, Department ofBiology, KSTC, Emporia, Kansas, 66801.

John Bulger, Wild Rivers of North America, January31, 1967

Albert Wool, Ranch Life and Wildlife, March 20,1967.

Patricia Bailey Witherspoon, Colorado Through the Seasons, April 20, 1967.